4

Logic

Logic is the study of reasoning and is specifically concerned with whether a particular reasoning is valid. It is a science of the necessary laws of thought, without which no employment of the understanding and the reason takes place.

4.1 PROPOSITIONS

Definition 4.1

A declarative sentence that is either true or false, but not both is called a Proposition or a Statement.

EXAMPLE 4.1

Which of the following are propositions?

  1. London is the capital of France
  2. Open the door
  3. Take two tablets of medicine
  4. x + y > 0, x, yZ
  5. The only positive integers that divide a prime number are 1 and the number itself.
  6. The sun is hot

Solution.

  1. The sentence is declarative and false. Hence, it is a proposition.
  2. The sentence “Open the door” is not declarative. ...

Get Discrete Mathematics now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.